In recent years, the number of vehicles equipped with vehicle control systems such as ABS (anti-lock brake system), TCS (traction control system), VSC (vehicle stability control system), and the like are rising to obtain the stability and safety of moving vehicles. In order to control these systems, it is necessarily to understand accurately the rolling situation of moving vehicle.
Then, the present applicants propose, in a Patent document 1, a technique to estimate back-and-forth direction force Fx, lateral force Fy, vertical force Fz acting on a tire by arranging plural of strain sensors on a side wall portion of the tire and estimating the strain of the sidewall portion.    Patent document 1: Japanese Unexamined Patent Application Publication No. 2005-126008.
In this technique, strains of three fixed points on the sidewall portion area measured at the same time with the strain sensors. And, calculate the back-and-forth direction force Fx, lateral force Fy, vertical force Fz basing on the three strain outputs t1, t2, and t3 according to the following determinant (1). The A1 to A3, B1 to B3, and C1 to C3 in the determinant are coefficients determined by means of tire loading test conducted beforehand.
                              [                                                    Fx                                                                    Fy                                                                    Fz                                              ]                =                                            [                                                                                          A                      ⁢                                                                                          ⁢                      1                                                                                                  B                      ⁢                                                                                          ⁢                      1                                                                                                  C                      ⁢                                                                                          ⁢                      1                                                                                                                                  A                      ⁢                                                                                          ⁢                      2                                                                                                  B                      ⁢                                                                                          ⁢                      2                                                                                                  C                      ⁢                                                                                          ⁢                      2                                                                                                                                  A                      ⁢                                                                                          ⁢                      3                                                                                                  B                      ⁢                                                                                          ⁢                      3                                                                                                  C                      ⁢                                                                                          ⁢                      3                                                                                  ]                                      -              1                                ⁡                      [                                                                                t                    ⁢                                                                                  ⁢                    1                                                                                                                    t                    ⁢                                                                                  ⁢                    2                                                                                                                    t                    ⁢                                                                                  ⁢                    3                                                                        ]                                              (        1        )            
However, when actually conducting a vehicle controlling such as ABS brake controlling for example, to speed up responsivity and conduct high performance vehicle controlling, obtaining information of force acting on the tire 8 times per one revolution, that is to say, each rolling angle of not less than 45 deg.